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Question

The following table represents undergraduate students at a local university. One student is chosen at random. Give your answer as a decimal out to at least 4 places.

	Freshman	Sophomore	Junior	Senior	Total
Live On Campus	4370	3888	1011	2885	12154
Live Off Campus	2544	4721	2535	2652	12452
Total	6914	8609	3546	5537	24606

a) Find the probability that the student lives off campus or is a junior. Correct

b) Find the probability that the student lives on campus and is a senior. Correct

c) Find the probability that the student is a freshman given that they live on campus. Correct

d) Find the probability that the student is not a senior. Correct

e) What percent of students that live on campus are juniors? Round percent to two decimal places.

Answer 1

Hi Lakotah,

a. Use the General Addition Rule:

P(A or B)= P(A) + P(B) - P(A and B)

A=Junior

B=Off-Campus

P(A)= 3546/24606

P(B)= 12452/24606

P(A and B)= 2535/24606--look at cell in row 2, column 3

P(A or B)= (3546/24606) + (12452/24606) - (2535/24606)

I will leave that computation to you.

b. Look at cell in first row, fourth column. That is the cell for seniors living on campus. Divide by total sample size 24606:

2885/24606 = 0.1172

c. This is Bayes' Theorem:

P(A given B)= P(A and B)/ P(B)

A=Freshman

B=Live on Campus

P(A) = 6914/24606

P(B)= 12154/24606

P(A and B) = 4370/24606--look in row 1, column 1.

P(A given B)= [4370/24606] / [12154/24606]

You can do those computations, and you will have the probability that student is a freshman given that they live on campus.

d. This is the Complement Rule aka the One Minus Trick:

P(A^C)= 1 - P(A)

A=Student is a senior

A^C=Student is not a senior

P(A)= 5537/24606

P(A^C)= 1-[5537/24606]

Do that computation, and you will have the probability of a non-senior in the sample.

e. Here, we just read the table. The total number of students who live on campus is 12154. The number of juniors who live on campus is 1011 (Row 1, column 3). So divide:

P= 1011/12154 = 0.0832

Now, we want a percent, so we multiply by 100:

P = 8.32%

I hope this helps.

Answer 2

P(off campus or junior) = P(~c v j) = P(~c) + P(j) - P(~c&j) = 12452/24606 + 3546/24606 - 2535/24606

= (12452 +3546 - 2535)/24606 = about .547143 = 54.7143% chance of off campus or junior selected

P(on campus & senior) = P(c&s) = 2885/24606 = about .117248 = 11.7248% chance on campus & senior

P(freshman/on campus) = P(f/c) = 4370/12154 = about ..359552 = 35.9552% chance freshman on campus

P(not a senior) = 1-P(s) = 1-5537/24606 = 19069/24606 = about .774974 = 77.4974% chance not senior

P(junior/on campus) = P(j/c) = 1011/12154 = about .0832 = 8.32% of on campus students are juniors